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Optimal controlled sampling designs that minimize the probability of selecting nonpreferred sample are obtained. These plans satisfy either of the following two require ments: (i) match specified joint inclusion probabilities, Πij, associated with an uncon trolled sampling plan having certain desirable properties; (ii) match specified first-order inclusion probabilities and provide stable, nonnegative unbiased variance estimators. Limitations of other approaches using methods of experimental designs are demonstrated.
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Rao et al. (1990) studied this question.
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